Design of Input-Output Observers for a Population of Systems with Bounded Frequency-Domain Variation using $DK$-iteration

This paper proposes a linear input-output observer design methodology for a population of systems in which each observer uses knowledge of the linear time-invariant dynamics of the particular device. Observers are typically composed of a known model of the system and a correction mechanism to produce an estimate of the state. The proposed design procedure characterizes the variation within the population in the frequency domain and synthesizes a single robust correction filter. The correction filter is compatible with all system models that satisfy the variation characterization such that a given level of estimation performance is guaranteed. This is accomplished by posing a robust performance problem using the observer error dynamics and solving it using $DK$-iteration. The design procedure is experimentally demonstrated on a flexible joint robotic manipulator with varied joint stiffnesses. It is shown that the proposed method that uses a single correction filter achieves comparable estimation performance to a method that uses a correction gain tailored toward each joint stiffness configuration.